Theorem eel2131

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016)

	Ref	Expression
Hypotheses	eel2131.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
	eel2131.2	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
	eel2131.3	⊢ ( ( 𝜒 ∧ 𝜏 ) → 𝜂 )
Assertion	eel2131	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜂 )

Proof

Step	Hyp	Ref	Expression
1		eel2131.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		eel2131.2	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
3		eel2131.3	⊢ ( ( 𝜒 ∧ 𝜏 ) → 𝜂 )
4	1 2 3	syl2an	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜑 ∧ 𝜃 ) ) → 𝜂 )
5	4	3impdi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜂 )